Some Properties of Non-linear $\sigma$-Models in Noncommutative Geometry

Abstract

We introduce non-linear $\sigma$-models in the framework of noncommutative geometry with special emphasis on models defined on the noncommutative torus. We choose as target spaces the two point space and the circle and illustrate some characteristic features of the corresponding $\sigma$-models. In particular we construct a $\sigma$-model instanton with topological charge equal to 1. We also define and investigate some properties of a noncommutative analogue of the Wess-Zumino-Witten model.

15 pages, latex. Talk presented at the Euroconference ``Hopf algebras and noncommutative geometry in field theory and particle physics'' Torino, September 1999. In v2 there are minor corrections and a ref added

References in corpus (1)

• Monopoles and Solitons in Fuzzy Physics

Cited by in corpus (16)

• Holomorphic structures on the quantum projective line
• Exact solitons on noncommutative tori
• Some properties of the integrable noncommutative sine-Gordon system
• D=2, N=2, Supersymmetric theories on Non(anti)commutative Superspace
• Sigma-model solitons on noncommutative spaces
• Non-linear sigma-models in noncommutative geometry: fields with values in finite spaces
• Fuzzy Nambu-Goldstone Physics
• Ultraviolet properties of noncommutative non-linear sigma-models in two dimensions
• Star product formula of theta functions
• Mapping spaces and automorphism groups of toric noncommutative spaces
• Solitons on Noncommutative Torus as Elliptic Calogero Gaudin Models, Branes and Laughlin Wave Functions
• Categories of holomorphic line bundles on higher dimensional noncommutative complex tori
• Noncommutative Nonlinear Sigma Models and Integrability
• Noncommutative Wess-Zumino-Witten actions and their Seiberg-Witten invariance
• Axial Gauged Noncommutative U(2)/U(1) Wess-Zumino-Witten Model
• Functor of Points and Height Functions for Noncommutative Arakelov Geometry